This is a review of recent developments regarding the Skyrmion sector of
higher representation QCD. Ordinary QCD is a SU(n) gauge theory with n_f Dirac
quarks in the fundamental representation. Changing the representation of quarks
leads to different and interesting theories, which are not as well studied as
ordinary QCD. In order to be able to have a consistent asymptotically free
large n limit, we must limit ourselves to three cases: two-index representation
(symmetric or anti-symmetric) and adjoint representation. Skyrmions of the
low-energy effective Lagrangian shall be the main subject of this review. There
are puzzling aspects, both in orientifold and adjoint QCD, regarding the
identification of the Skyrmion and its quantum stability, that have not yet
been understood. We shall explain these problems and the solution we proposed
for them. The first part is dedicated to the two-index representation. Here the
challenge is to identify the correct particle in the spectrum that has to be
identified with the Skyrmion. It turns out not to be the simplest baryon (as in
ordinary QCD) but a baryonic state with higher charge, precisely composed by
n(n\pm 1)/2 quarks. Although not the simplest among the baryons, it is the one
that minimizes the mass per unit of baryonic charge and thus is the most stable
among them. The second part is devoted to the quarks in the adjoint
representation. The task here assume a different perspective. We do not have a
baryon charge, like in ordinary QCD. An important role is now played by a
massive fermion that must be considered in the low-energy effective Lagrangian.
Through this fermion, the Skyrmion acquires an anomalous fermionic number
(-1)^F and, as a consequence, an odd relationship between the latter and its
spin/statistic. This implies a Z_2 stability of the Skyrmion.Comment: 38 pages; 15 figures. v2: ref adde
